The elements of this Hilbert space are n-dimensional complex valued
vectors with the usual inner product that takes the complex conjugate
of the vector on the right.

A classic example of this type of Hilbert space is spin-1/2, which is
ComplexSpace(2). Generalizing to spin-s, the space is
ComplexSpace(2*s+1). Quantum computing with N qubits is done with the
direct product space ComplexSpace(2)**N.